Seventh Grade · Math · week 22

Two-step inequalities

Solve two-step inequalities, correctly flipping the inequality symbol when multiplying or dividing by a negative number.

Two-step inequalities solve exactly like two-step equations, with ONE extra rule: whenever you multiply or divide both sides by a NEGATIVE number, you must flip the inequality symbol. Adding or subtracting never flips it.

A quick way to test your flip is to plug in a simple number from your answer's range back into the ORIGINAL inequality -- if it makes the statement true, the direction is correct.

📋 For the teacher
Teach it (10–15 min):
  • Make the flip rule impossible to miss: say "multiply or divide by a negative? Flip the symbol!" out loud every single time it applies.
  • Practice a matched pair, one positive coefficient and one negative, side by side so the difference is obvious.
  • Use the plug-a-number check often this week -- it builds real confidence that the flip was applied correctly.
  • Connect two-step inequalities to a real budget or speed limit scenario so the direction of the answer makes intuitive sense.
Talk about it:
  • When exactly do you flip the inequality symbol?
  • Why does dividing by a negative number flip the direction of the inequality, while adding or subtracting never does?
  • How can plugging in a number check whether your answer's direction is correct?

Mastery looks like: They solve a two-step inequality correctly, flipping the symbol only when multiplying or dividing by a negative number.

Common stumbles: Flipping the symbol when adding or subtracting a negative number (not required); forgetting to flip when dividing by a negative coefficient.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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